We consider here a system of non-relativistic particles. It follows with little surprise then that the notion of time that we adopt here shares some formal similarity with the Newtonian view of time. For instance, it is well known (see e.g., [1]}) that a Newtonian theory can be formulated as a fiber bundle. The construction is the following: we can take the time \(t\in \mathbb {R}\)  to be the base manifold and take each fiber to be a copy of real space \(\mathbb {R}^{3}\) . (In addition, each fiber is also endowed with a Galilean symmetry group.) Looked at from this angle, it is clear that a single number \(t\in \mathbb {R}\)  specifies an instant of time to which we associate a copy of three-dimensional Euclidean space; this, in turn, makes it explicit that each point \(\vec{x}\in \mathbb {R}^{3}\)  is simultaneous with one another in Newtonian physics.
